Some Bilinear Stochastic Equations with a Fractional Brownian Motion

T. E. Duncan ()
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T. E. Duncan: University of Kansas

Chapter Chapter 6 in Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, 2006, pp 97-108 from Springer

Abstract: Abstract An explicit solution is given for a bilinear stochastic differential equation with a fractional Brownian motion that is described by noncommuting linear operators and that has the Hurst parameter H in the interval (1/2, 1). It is shown that the expression for this family of solutions for H in (1/2, 1) extends to the solution for a Brownian motion, H = 1/2. Some examples are given to contrast the solutions for commuting and noncommuting linear operators, in particular, the asymptotic behavior of the solutions can be significantly different for commuting and noncommuting operators. The methods to obtain the explicit solutions use a stochastic calculus for a fractional Brownian motion and some Lie theory.

Keywords: Fractional Brownian motions; bilinear stochastic differential equations; explicit solutions of stochastic equations (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-0-387-33815-6_6

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DOI: 10.1007/0-387-33815-2_6

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